Interactive

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Thinkport | Simple Random Sampling

Gather random samples and use them to make inferences about the percentage of blue candies in a jar in this interactive from MPT. In the accompanying classroom activity, students use the interactive and then use random sampling to explore a question involving hands-on materials in the classroom. They compare results from different samples and then make appropriate inferences. To get the most from the lesson, students should be comfortable expressing a fraction as a percentage and be familiar with the notion of a random sample. For a longer self-paced student tutorial using this media, see "Simple Random Sampling" on Thinkport from Maryland Public Television.

Materials: Per pair: pencils, a bowl containing 50 to 100 objects identical except for color (e.g., the contents of a bag of candy in five different colors); Random Samples activity sheet; for the class: a clear jar filled with the chosen objects to use for demonstration

Note: For the purposes of explaining the lesson, we use red as an example of one of the colors of the objects. Any five different colors will suffice.

Preparation: Decide on a question for students to investigate with the objects, for example, What percentage of these candies are red? Fill in the blanks on the activity sheet to reflect your question, and then make copies. Fill each bowl for the activity with the same mix of colors (e.g., same brand/size candy bag).

Procedure1. Introduction and Interactive (10 minutes, whole group) Pass around the demonstration jar and ask students to predict the answer to the question you prepared.

Explain that students will use simple random sampling to find a reasonable answer without counting each item.

Display Screen 1 of the interactive and ask students to predict the percentage of blue (marked with B) candies.

Work through the interactive with the class, pausing to introduce the terms population, characteristic of interest, frequency and to engage students in discussing the following:

Screen 4. Why is it important to use the same size sample?

Screen 7. Do you think that you could end up with no blue candies? All blue candies?

Screen 13. How many of you predicted more than 13%? Less than 13%?

Screen 14. What can you tell from this graph? Do the samples vary much? How do you know?

2. Random Sampling (15 minutes, pairs and whole group) Distribute the materials and review the instructions for the activity sheet. As students work in pairs, circulate to encourage them to consider whether their samples are representative and why.

When everyone is finished, ask one member of each pair to participate in a human bar graph that shows the average percentage of (red candies) in their samples. For instance, all those with 20% line up to form a bar, those with 25% red make a line next to them, and so on. Prompt those in the audience to note the range, mode, and any outliers. Then ask, What inferences can we make about the percentage of red in:

our samples?

this (demonstration) jar?

bags of this type of candy for sale in the grocery store?

If time permits, engage students in counting the number of red candies and total number of candies in their jars to determine the accuracy of the sampling method.

3. Conclusion (5 min, whole group) Wrap up with a few reflection questions, such as:

Why is it important to take samples of the same size?

How can you tell if samples are representative?

What can you infer from a representative sample?

Activity Extension: Have students plan a way to investigate a question via random sampling (e.g., the average length of a Top 100 song). They should gather random samples and consider what they can infer about the population under study.